1

Part of 2015 Nordic

Problems(1)

circle with diameter a side of a triangle

Source: Nordic Mathematical Contest 2015 #1

{ABC}

be a triangle and

{\Gamma}

the circle with diameter

{AB}

. The bisectors of

{BC}

{\angle ABC}

{G}

{D, E, F}

{E}

, respectively. The incircle of

{ABC}

{BC}

{AC}

{F}

{G}

, respectively. Prove that

{D, E, F}

{G}